Course Details - Mathematics and Statistics - Penn State Altoona

Math 220

Matrices

2 credits

Blue Book Description: Systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations.

Pre-requisites: Math 110 or 140

Pre-requisite for: Math 310, Math 484

Suggested Textbook:
Linear Algebra and Its Applications, 3rd Edition, by David C. Lay, published by Addison Wesley.
Check with your instructor to make sure this is the textbook used for your section.

Topics:
Chapter 1: Linear Equations in Linear Algebra
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Form
1.3 Vector Equations
1.4 The Matrix Equation Ax=b
1.5 Solution Sets of Linear Equations
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models (optional)

Chapter 2: Matrix Algebra
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.7 Applications to Computer Graphics (optional)
2.8 Subspaces of Rn
2.9 Dimension and Rank

Chapter 3: Determinants
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule (optional)

Chapter 4: Vector Spaces
4.1 Vector Spaces and Subspaces (optional)
4.4 Coordinate Systems
4.7 Change of Basis

Chapter 5: Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations (optional)
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems (optional)
5.7 Applications to Differential Equations (optional)

Chapter 6: Orthogonality and Least Squares
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
6.5 Least-Squares Problems (optional)

Chapter 7: Symmetric Matrices and Quadratic Forms (optional)
7.1 Diagonalization of Symmetric Matrices (optional)